This is a combinatorial notation for what elsewhere is termed the Kronecker Delta function. Here \([n=m]\)  is 1 when \(n=m\)  and 0 otherwise. This is called Iverson's convention in [1]}. For a discussion of the merit of this notation, see [1]}. The Legendre polynomials satisfy the three term recursion relation
\((n+1)P_{n+1}-(2n+1)P_n+nP_{n-1}=0\) 
